Mass-Invariant Universal Optical Conductivity from Quantum Geometry

Mass is a defining property of particles, shaping their fundamental nature and interactions. In condensed matter systems, the effective mass of electrons has long been regarded as a key factor influencing material properties, including their transport and optical responses. In this work, we challenge this conventional wisdom by unveiling a mass-invariant universal optical conductivity, purely derived from quantum geometry, in quadratic band-touching semimetals.

Specifically, the optical conductivity simplifies to $\sigma = (e^2/8\hbar)d^2_\mathrm{max}$, independent of effective mass and other band structure details, where $d_\mathrm{max}$ represents the maximum Hilbert-Schmidt quantum distance.

Furthermore, under time-reversal and rotational symmetries, $d_\mathrm{max}$ is restricted to discrete values of 0 or 1, leading to a quantized universal optical conductivity.

We also use first principles calculations to demonstrate the mass-invariant universal optical conductivity across multiple materials, including bilayer graphene, monolayer bismuth, monolayer kagome Pd$_3$P$_2$S$_8$, and other realistic material candidates.

Our work establishes a new class of universal quantities in quantum materials entirely governed by quantum geometry.